Exam 15: Multiple Integrals

Use spherical coordinates to evaluate where B is the ball

Find the area of the surface.The part of the sphere that lies above the plane

Identify the surface with equation

Select the correct Answer for each question. -Use spherical coordinates.Evaluate where is the ball with center the origin and radius

Select the correct Answer for each question. -An electric charge is spread over a rectangular region ind the total charge on R if the charge density at a point in R (measured in coulombs per square meter) is

Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis.

Select the correct Answer for each question. -Calculate the iterated integral.

Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane

Select the correct Answer for each question. -Find the area of the part of hyperbolic paraboloid that lies between the cylinders

Find the mass and the moments of inertia and the radii of gyration for the lamina occupying the region R, where R is the region bounded by the graphs of the equations and having the mass density

Select the correct Answer for each question. -Use polar coordinates to find the volume of the solid under the paraboloid and above the disk

Select the correct Answer for each question. -Find the area of the surface.The part of the surface that lies above the xy-plane.

Find the volume of the solid bounded by the surface and the planes and coordinate planes.

Use the given transformation to evaluate the integral. where R is the region in the first quadrant bounded by the lines and the hyperbolas

Evaluate the double integral is the region bounded by the graphs of

Calculate the double integral.Round yourAnswer to two decimal places.

Sketch the solid bounded by the graphs of the equations and and then use a triple integral to find the volume of the solid.

Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis.

Select the correct Answer for each question. -Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density

Select the correct Answer for each question. -Evaluate the integral and with respect to in that order.